MythBusters did two tests: one was with weather balloons, and one with party balloons.
The weather balloon one was confirmed; they did get Adam airborne (albeit tethered) in a lawn chair. For safety, they reinforced the chair.
The party balloon story was the sitcom staple of a balloon vendor's bundle carrying away a small child. (They used a clip from Mr. Bean to illustrate it.) This was busted. It took 3500 balloons to get a 44lbs. child off the ground.